Evaluate lim_(x -> 2) (x^2 - 4) / (x - 2).
Answer and explanation
Correct answer: A. 4
- Step 1: Direct substitution gives 0/0, so factorise: x^2 - 4 = (x - 2)(x + 2).
- Step 2: Cancel (x - 2): the limit becomes lim (x + 2) as x -> 2.
- Step 3: Substitute: 2 + 2 = 4.
Answer
4.
Why not the others: '2' gives the value of k instead of the sum k + k; '0' treats the 0/0 form as equal to zero instead of simplifying; '5' adds one in the factorisation.
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